matt has started a car washing bussiness to save money for college. each week , he washes 3 more cars than he did the week before

Question

matt started by washing 6 cars his first week in business write a explicit formula that can be used to find the number of cars he washed on any given week
a. a n = 6 _= 6 + 3n
b . a n = 6(3n-1)
c . a n = 6 + 3 ( n - 1
d. a n = 3 + 6 ( n - 1)

Answer 1

To derive the explicit formula for the number of cars Matt washes in any given week, we need to analyze his pattern of washing cars.

Matt washes 6 cars in the first week, and each week thereafter he washes 3 more cars than the previous week. This means:

• Week 1: 6 cars
• Week 2: 6 + 3 = 9 cars
• Week 3: 9 + 3 = 12 cars
• Week 4: 12 + 3 = 15 cars
• ...

If we observe this pattern, we can establish that the number of cars washed in week \( n \) can be expressed as follows:

1. In the first week (\( n = 1 \)), he washes 6 cars.
2. In the second week (\( n = 2 \)), he washes \( 6 + 3(1) \) cars.
3. In the third week (\( n = 3 \)), he washes \( 6 + 3(2) \) cars.
4. In the \( n \)-th week, he washes \( 6 + 3(n-1) \) cars.

So, the explicit formula to find the number of cars washed in any given week \( n \) is:

\[ a_n = 6 + 3(n - 1) \]

Thus, the correct answer is c. \( a_n = 6 + 3(n - 1) \).